The Ontological Argument is Sound

You are conflating "conjuring mental images of a scenario/world" with coming up with a logically consistent scenario/world.

The latter is closer to what is required for the modal ontological argument to work, which uses metaphysically possible world semantics.

It might not make sense to you to not be able to conjure mental images of the absence of something, but it makes perfect sense to create a logically consistent scenario where something is absent.

I can conceive of a cupboard that is empty, and one that contains a broom.

I can even go as far as to conjure mental images of exactly that, too.

The statement "Existence is epistemologically rational; nonexistence is not" is one of the most absurd things I have ever read, and I have never seen a single philosopher, theist or otherwise that has ever asserted that on any level, and I have ready plenty of their papers.

Luckily "perception" (whhich I take to be just conjuring mental images) and "interaction" are not prerequisites of conceiving a logically consistent world with something absent.

Their non-existence in the cupboard, yes it does.

1. A world that contains nothing, zilch, zero.

Or more compellingly:

2. A world that contains a single particle, that just exists as is, and does nothing. You can even go a step further and have a particle that exists eternally in one spacial dimension that simply evolves over time with De Broglie motion. That way you have a complete world that can be described with a single mathematical equation, perfectly logically consistent, and it's logical consistency isn't broken by the absence of a maximally great being.

I can readily conceive mathematically of these self-contained worlds. I can even conjure mental images of each, but again this isn't a requirement for something to be logically or metaphysically possible.

Your second premise is erroneous. Since your second premise operates on applying superlatives to the qualifiers, "greater," and "more" from the first premise, then the second premise should read as such: "Since the MGB is the greatest being, it would convince the most that it exists." Using your revised premise, your third premise is no longer substantiated since the second premise no longer requires that you be convinced that the MGB exists. Given that your second premise has been revised, and your third premise has been rendered unsubstantiated, your conclusion is nullified.

Furthermore, C2 is also unsubstantiated even if your second premise was valid. The MGB exists as outlined by the parameters of your first premise. You can argue that the subject doesn't meet those parameters, but that does not permit you to posit that the MGB doesn't exist without undermining your first premise.

There is no contradiction in the argument you reference. The contradiction is actually in your response, "it is also possible to think of a world where the MGB doesn't exist." It begs the question: how do you think about something that doesn't exist if it doesn't exist? How do you conceive a world where you acknowledge the nonexistence of the MGB, when nonexistence cannot be perceived? Existence is epistemologically rational; nonexistence is not.

Do you agree that a being that can convince X people is greater than one that can convince X - 1 people?

If nothing that exists can possibly fit the criteria of X, then X doesn't exist.

I never said one could conceive of a world where everyone acknowledges the nonexistence of the MGB. I said that one could conceive of a world where the MGB doesn't exist (as P1 states).

It isn't anymore nonsensical to conceive of a world where the MGB doesn't exist then it is to conceive of a world where cellphones don't exist.

All that my argument says is that it states there is possible to conceive of a world where X doesn't exist, which is completely in line with P1.

Greater in which context?

How do you know that nothing that exists can possibly fit the criteria of X? Was your argument not extending the first premise which focused on a single being?

Acknowledging nonexistence is paradoxical. How can one then conceive a world in which something does not exist, if it does not exist? That is, in this world you've conceived, how is one able to qualify this world with the description, "MGB does not exist," if one cannot acknowledge its nonexistence? So even in a world you conceive where the MGB is displaced  (not nonexistent) you are acknowledging MGB in your posit of its "absence."

You can't conceive a world where cellphones don't exist. You can conceive their displacement and lack of use, using your own experience as information. But you have no experience with the nonexistence of cell phones; therefore, you cannot conceive a world in which they do not exist.

And my argument claims that this is impossible because perceiving--even conceiving--nonexistence is epistemologically irrational.

Greater in the context of the MGB.

C1: Since there is at least one person that is not convinced of the MGB's existence (me), it cannot be the MGB.

If P2 is valid, then P3 is too. C1 states that since the MGB (as defined in P1 and P2) cannot fulfill its "maximal greatness" (it would be required to in order to be the MGB), it isn't the MGB. Since nothing that exists can fit the definition of MGB (as shown in P3 in contrast to the definitions of P1 and P2), the MGB would not exist.

The first cellphone came into existence in 1983. Before then, cellphones didn't exist. So, if one can conceive of a world before 1983 (which is entirely possible), then one can conceive of a world where cellphones don't exist.

I have just shown with my example above that it is possible.

Then by your stipulation, my agreement would be irrelevant.

Yes, but P3 does not allow you to infer that "nothing that exists can fit the definition of MGB." It only stipulates that you be convinced.

Before 1983, no one knew cellphones didn't exist because cellphones didn't exist. Any retrospective analysis which seeks to relate experiences before and after the creation of cellphones would not be a conception void of their existence because the analysis itself is fundamentally based on the fact that cellphones do exist.

It was a rhetorical question. I used it to show that "the most" people = everyone. Unless you can show how this is impossible, that would be the case.

There would only be a being called MGB (as defined in P1 and P2) if it can convince everyone (as demonstrated by above)

Since I am part of the group called "everyone", and it hasn't convinced me of its existence, the "MGB" fails to be the MGB, because it hasn't met the condition to be the MGB.

I didn't say one could conceive of a world where people knew of the nonexistence of cellphones, I said that one could conceive of a world where they don't exist, period.

P1: Entity X comes into existence in time Y. 

P2: Before time Y, X did not exist (restatement of P1). Let's call this time Z.

P3: X does not exist in time Z. (restatement of P2)

P4: It is possible to conceive of a world as it was during time Z.

C1: Therefore, it is possible to conceive of a world where X does not exist.

Non sequitur. I did not argue that it was impossible for most to reflect everyone. Most however does not require everyone. It's a relative superlative.

And given that your first premise stipulates that the MGB's greatness is contingent on its capacity to convince more people than the the next being, then it need only convince more people than every other being.

You didn't demonstrate anything.

Only if the superlative necessarily reflects everyone. And it doesn't. Your second premise is invalid.

How? If the world which they conceive is one in which cellphones don't exist, they cannot know this because they don't exist. So then how can one conceive this world and apply the description, "cellphones don't exist," if they can't know that cellphones don't exist given that they don't exist?

P1: Entity X is created in time Y.

P2: Before time Y, Entity X wasn't created. This will be called time Z.

P3: Entity X was not created in time Z.

P4: Conception is current.

P5: Conception (retrospective analysis) of a world during time Z will occur in and with respect to time Y (presuming Y constitutes all time since the cellphone was created.)

P6: Conception of the World at time Z, during time Z, is not possible. (Z is past, Conception is current.)

C: Therefore, conception of a world where Entity X did not exist is impossible.

Luckily "perception" (which I take to be just conjuring mental images) and "interaction" are not prerequisites of conceiving a logically consistent world with something absent.

Yes they are. Because you would have to acknowledge (perceive) the absence of that something with no experience or data to inform its placement or displacement, its form or its being, because as that which is characterized as "absent," it does not exist.

Their non-existence in the cupboard, yes it does.

Once again, you're attempting to inform location, not existence.

1. A world that contains nothing, zilch, zero.

Then it isn't a world if it contains "nothing." Remember you stated, "The latter is closer to what is required for the modal ontological argument to work, which uses metaphysically possible world semantics."

Or more compellingly:

2. A world that contains a single particle, that just exists as is, and does nothing. You can even go a step further and have a particle that exists eternally in one spacial dimension that simply evolves over time with De Broglie motion. That way you have a complete world that can be described with a single mathematical equation, perfectly logically consistent, and it's logical consistency isn't broken by the absence of a maximally great being.

I can readily conceive mathematically of these self-contained worlds. I can even conjure mental images of each, but again this isn't a requirement for something to be logically or metaphysically possible.

How do you acknowledge the absence of the MBG if it is in fact absent?

in the context of the MGB, a being is greater than another if it can convince more people of its existence.

Since the MGB is the "Maximally Great Being", it would have to convince the maximum number of beings of its existence.

Do you agree that a being that can convince X people is greater than one that can convince X - 1 people?

My argument stated, that in the context of the MGB, a being is greater than another if it can convince more people of its existence. If a being can convince X + 1 people of its existence, then it is greater, by definition. A maximally great being would thus have to be maximally great in this regard, meaning that it is not possible to be any greater than it, by definition. The only way for it to be impossible for another being to convince X + 1 people of its existence is if X already contains the entire set of the population since it is impossible to have an attribute (such as being convinced) apply to more items than there are items entire set. 

No. Since the MGB is the "Maximally Great Being", it would have to convince the maximum number of beings of its existence. Unless you can show how it is impossible for the maximum number of beings to mean every being, then it would have to mean every being, since if it doesn't, then there would be more beings that could be convinced.

See points 1 and 2 of this post.

Why does the conceiving of a world where X doesn't exist mean that the beings in that world acknowledge its non-existence?

P5 is faulty. The act of conception happens in the current time (and thus would be in respect to time Y), but the subject that is being conceived isn't in current time. The conception of Z occurs in time Y, but since it has it's own setting, the subject matter itself wouldn't be in respect to time Y. The timeline of the world at time Z would also follow the timeline of Z, not of Y.

No you don't. Please prove that rather than just asserting it. This is a ridiculous argument.

This is trivial in set theory, it's used all the time in math. I can create a set containing only elements A, B and C, I do not be able to perceive an imaginary element D to state that this set contains only the elements A,B and C. Here is the description of "Set X"

Definition:

Set X: 1. Contains only A, B, C

Definition: Set Y:

Contains D

Set Y =/= Set X. Neither does set Y contain set X.

So you can assert that something exists (D) in a set containing the elements A, C and C but then you are no longer talking about Set X, you are talking about Set Y, which does not contain set X. You have just created a new set instead.

To continue this, we can make another set:

Set Z: Contains A, B. C, D

What can we say about Set Z? Well set Z is a subset of set Y. It is not a subset of set X though.

There is no broom in the cupboard... No broom exists in the cupboard. 

Really? And in what philosophical journal have you read that?

If the question "why is there something rather than nothing?" is to make sense then it must be possible for there to be a universe in which nothing exists.

There is nothing logically inconsistent a priori with that.

That's the reason why both theologians and physicists pose that question in the first place.

It certainly is a far more well-accepted state of affairs than a metaphysically possible world containing a metaphysically necessary being in it. The former is largely accepted by atheists and theologians, the latter is only accepted by a small fraction of theologians.

Because you have a complete and consistent description of a logically possible world without a MGB being in it...

You would need to show that such a world is inconsistent for it not to be a logically possible world.